Question: What do the following two equations represent? $2x-5y = 5$ $4x-10y = -5$
Solution: Putting the first equation in $y = mx + b$ form gives: $2x-5y = 5$ $-5y = -2x+5$ $y = \dfrac{2}{5}x - 1$ Putting the second equation in $y = mx + b$ form gives: $4x-10y = -5$ $-10y = -4x-5$ $y = \dfrac{2}{5}x + \dfrac{1}{2}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.